BRDF CORRECTION ON AVHRR IMAGERY FOR SPAIN
H. Heisig
Institut für Photogrammetrie und Fernerkundung, Universität Karlsruhe, D-76137 Karlsruhe heisig@ipf.uni-karlsruhe.de
TS 3 YF Youth Forum - Remote Sensing
KEY WORDS: Remote Sensing, Radiometry, Correction, Model, Land Cover
ABSTRACT
The free reception of Advanced Very High Resolution Radiometer (AVHRR) data keeps a growing interest for the remote sensing
community concerned with vegetation studies on regional and global scales. However, the use of AVHRR data for long-term
quantitative monitoring requires consistent surface reflectance data. This implies correcting the effects from varying sun sensor target
geometries in multitemporal AVHRR data sets described by the Bidirectional Reflectance Distribution Function (BRDF). In a joint
research undertaken by the Geography Department of the University of Alcalá (Spain) and the Canadian Centre for Remote Sensing
(CCRS) a new semi-empirical model, the Non-linear Temporal Angular Model (NTAM), has been applied for the BRDF correction
of AVHRR data for Spain. Reflectance data derived from AVHRR channels 1 and 2 were corrected for BRDF effects by
normalization to a standard viewing geometry. The study period was between May and September 2002. The required correction
parameters were derived by model inversion. In order to obtain a good representation of the temporal and spatial dimensions of the
data to be corrected, a sampling scheme was implemented. The land cover based approach of the NTAM was accounted for by the
use of CORINE Land Cover data from Spain. A cloud mask algorithm was used to exclude cloud contaminated observations in the
sampling data. The evaluation of the statistical parameters obtained from model inversion showed good results for practically all land
cover classes in the two channels. Derived parameters allow for visualization of angular dependence of reflectance for different land
cover classes.
1. INTRODUCTION
Current research work at the Geography Department at the
University of Alcalá is strongly focussed on the field of fire risk
assessment (Chuvieco 2002). Since 1998 the department
receives AVHRR data in the High Resolution Picture
Transmission (HRPT) format through an own receiver. These
data are used for estimation of plant water content with the
purpose of incorporating these estimations in fire risk indices
(Aguado et al., 2003; Chuvieco et al., 2003).
Sun-synchronous polar-orbiting satellites like the National
Oceanic and Atmospheric Administration (NOAA) AVHRR
sensors are operated on must have such an orbital inclination
that the rate of the resulting precession compensates for the
motion of the Earth around the sun (Cracknell 1997). The
satellite’s orbit tracks projected on the Earth’s surface reveal a
parallel shift of about one degree east per day. This results in
changing view angles for the same target within consecutive
day passes.
BRDF
Vegetation, as most other surfaces, does not scatter irradiance
in equal quantities in all directions. In fact, it shows a behaviour
far from being Lambertian (Dymond et al., 2001). Its
reflectance depends on the angle of observation as well as on
the angle of the incidence of the solar radiation. This bidirectional dependency lead to the idea of the BRDF
(Bidirectional Reflectance Distribution Function). The BRDF
describes the ratio of radiance dLr [W m-2 sr-1 nm-1] reflected in
one direction (θr, φr) to the irradiance dEi [W m-2 nm-1] from
direction (θi, φi) (Sandmeier & Itten, 1999). Figure 1 displays
the angles that the BRDF is dependent on.
ξ
dLr
dEi
θr
θi
φr
φi
Figure 1: Concepts and parameters of the BRDF (Sandmeier &
Itten, 1999, modified)
where:
θi = zenith incidence angle
θr = zenith reflection angle
φi = azimuth incident angle
φr = azimuth reflection angle
ξ = phase angle
Parallel to the enhancement of BRDF measuring methods
(goniometers, measurements from helicopters), considerable
effort has been spent on development and testing of analytical
and empirical models to describe the BRDF (Chen & Cihlar,
1997; Chopping, 2000; Hu et al., 1997; Ni et al., 1999; Ni & Li,
2000; O’Brien et al., 1998; Roujean et al., 1992; Wanner et al.,
1995). BRDF models potentially allow for prediction of
reflectance for any desired sun sensor target geometry.
Because partial cloud cover is practically always existent on a
regional scale, different algorithms for creation of cloud-free
AVHRR composites were developed. The composites are
typically made from 10 day periods.
BRDF effects in AVHRR composite imagery can visually be
noted through a non-coherent and coarse structure as well as
striping effects. The normalization to a standard viewing
geometry potentially reduces significantly such effects. In the
case of correlation of different indices with field measured plant
water contents it is assumed that BRDF corrected AVHRR
imagery will yield better correlations and thus enhance the
certainty of predictions.
2. METHODOLOGY
2.1 Data sets
In this study, AVHRR data from NOAA 15 and NOAA 16
covering part or the whole Iberian Peninsula were used. The
daily NOAA 16 data acquisition time is between 3 and 4:30 pm,
data from NOAA 15 are usually received between 9:30 and
11:00 am. The data is received in the HRPT format through a
parabolic antenna. The data are calibrated as described by the
NOAA manuals (KLM Users Guide, 2000). In order to avoid
strong geometric and radiometric distortions, only data with a
scan angle smaller than 45° were used. The image data are
georeferenced and reprojected. The size of the imagery is 1136
by 889 pixels. The data sets used in this study were received
between May and September 2002.
2.2 Models
The model applied for normalization of AVHRR data in this
study is the NTAM (Non-linear Temporal Angular Model) as
described by Latifovic et al. (2003). It is based on the widely
used Roujean model (Roujean et al., 1992). The Roujean model
and the empirical modified Walthall model (MWM, Walthall et
al. 1985) are used for comparison of model performance. The
three models are defined as follows:
The Roujean model:
ρ (θ i ,θ r , φ ) = k 0 + k1 f1 (θ i ,θ r , φ ) + k 2 f 2 (θ i ,θ r , φ )
The modified Walthall model:
ρ (θ i ,θ r , φ ) = a0 (θ i 2 + θ r 2 ) + a1θ i 2θ r 2 + a2 cos(φ ) + a3
f 2 ( θ i , θ r , φ) =
4
1
*
3π cos θ i + cos θ r
 π
 1
( 2 − ξ) cos ξ + sin ξ  − 3


cos ξ = cos θi cos θ r + sin θi sin θr cos φ
α1 =
NIR − VIS
= NDVI
NIR + VIS
α 2 = NIR − VIS
and:
ρ = reflectance
φ = relative azimuth angle = |φ i - φ r|
j = land cover class
i = AVHRR channel (1 = VIS, 2 = NIR)
The Roujean model belongs to the important group of
physically based BRDF models that have reflectance as a linear
function of parameters (Shepherd & Dymond, 2000). It
considers the observed directional reflectance as the sum of a
geometric and a volume scattering component. The parameters
k0, k1 and k2 are semi-empirical coefficients representing
physical properties of the surface. They are often referred to as
‘kernels’ (Wanner et al., 1995). In model inversion k0, k1 and k2
are obtained on a per-pixel base through least squares fit
between model and observations by minimizing an error
function.
Because the BRDF is time-wise dynamic, derivation of the
model parameters in multitemporal data sets requires regression
techniques made in subperiods (Leroy & Roujean, 1994). The
number of cloud free observations within a sub period of about
10 days can thus easily become a limiting factor (Cihlar et al.,
2002). The Modified Walthall model is a purely empirical
model employing the four parameters a0, a1, a2 and a3.
The NTAM was designed at the Canadian Centre of Remote
Sensing (CCRS) for normalization of AVHRR imagery from
northern ecosystems (Chen & Cihlar, 1997; Cihlar et al., 2002).
The defined aim of this study is to investigate its applicability in
a Mediterranean environment. The NTAM modifies the
Roujean model to a time-independent, non-linear, physically
based 8 parameter BRDF model. Model inversion is to be
applied on land cover classes rather than on a per-pixel base.
The temporal dimensions of the NTAM are approximated by
polynomials that are related to vegetation indices. They account
for the varying green leaf area during the growing season and
the land cover dependent patterns of geometric and volume
scattering components (Latifovic et al., 2003).
The NTAM:

ρi (θi ,θ r ,φ,αi ) = 1 + a7,i ( j)e

ξ
π
− a8,i ( j )

*

1 + (a1,i ( j) + a2,i ( j)(1 −αi ) + a3,i ( j)(1 − αi )2 ) f1 (θi ,θ r ,φ)


2

+ (a4,i ( j) + a5,i ( j)αi + a6,i ( j)αi ) f 2 (θi ,θr ,φ)
2.3 Cloud Mask Processing
For the generation of cloud free input sampling data a cloud
detection algorithm based on the formulations of Saunders &
Kriebel (1988) is applied. The algorithm consists of five tests
that are applied to each individual pixel. A pixel is only
considered to be cloud free if all the tests prove negative.
2.4 Spatial sampling
where:
1
[(π − φ) cos φ + sin φ]tan θi tan θr
2π
1
− (tan θi + tan θr + tan2 θi + tan2 θr − 2 tan θi tan θr cos φ )
π
f1 (θi , θr , φ) =
The NTAM requires a database that assigns each pixel in the
imagery to a land cover class. In this study, CORINE Land
Cover data from Spain are used to assign land cover class
membership. CORINE Land Cover describes land cover based
on a nomenclature of 44 classes that are hierarchically
organised into three levels (CORINE Land Cover Report,
2000). These data were reprojected to fit projection and cell
size of the AVHRR imagery.
•
The coefficient of determination R2 defined by:
The original land cover types were aggregated into 14 land
cover classes to represent major structural and surface cover
combinations. For each aggregated land cover class between 60
and 100 sampling points were defined. Minimum distance to
pixels of other classes was 5 pixels, minimizing thus the effect
of transition pixels. For these sampling points the median
reflectance value from a 3*3 window were sampled. Table 1
lists the agglomerated CORINE Land Cover classes and their
relative fraction of the surface of Spain.
where:
δ2 =
1
N
2
δobs
=
•
N
∑ [ρ
i
− (ρ obs )i
]
2
i =1
1
N
1
(ρobs )i2 − 
i=1
N
N
∑

(ρobs )i 
i=1

N
∑
2
The standard error of the estimate (se) defined by:
%
coverage
23.08
7.53
2
N
∑ [ρ − (ρ ) ]
i
se =
obs i
i=1
N
where:
ρobs = observed reflectance
ρ = modelled reflectance
N = number of observations
3.13
8.39
5.23
4.73
6.88
9.00
2.11
5.54
3.54
10.27
6.45
2.42
3. RESULTS AND DISCUSSION
The CORINE Land Cover class 17 (olive grows), maybe the
most emblematic land cover for Spain, was chosen to
demonstrate the quality of the regression. In figure 2 modelled
and observed reflectance are displayed for the sampling data in
the NIR channel. 1052 observations were collected from NOAA
15 data and 852 observations originate from NOAA 16 data.
The data from the two sensors were inverted together. They are
displayed in different colours only for better legibility.
1.70
Table 1: CORINE Land Cover classes and relative fraction of
surface
2.5 Temporal and angular sampling
Data were sampled from cloud mask processed datasets from
throughout the study period. Between 1000 and 2000
observations per aggregated land cover class were obtained.
Alternatively to cloud mask processing, data might have been
sampled from cloud free composites.
modelled reflectance
Aggregated Comprises classes
class
12
12: Non irrigated arable land
13
13: Irrigated arable land
15: Vine yards
16: Fruit trees and berry plantations
17
17: Olive grows
20
18: Pastures
19: Annual with permanent crops
20: Complex cultivation patterns
21
21: Agriculture with natural
vegetation
22
22: Agro forestry areas
23
23: Broad leafed forests
24
24: Coniferous forests
25
25: Mixed forests
26
26: Natural grassland
27
27: Moors and heathland
28
28: Sclerophyllous vegetation
29
29: Transitional woodland shrub
31
31: Bare rock
32: Sparsely vegetated areas
0
All other classes (mainly
settlements)
δ2
δ 2obs
R2 = 1−
0,3
0,25
0,2
NOAA 15
0,15
NOAA 16
0,1
0,05
0
0
0,1
0,2
0,3
0,4
observed reflectance
2.6 Model inversion and statistic parameters
Figure 2: Observed and modelled reflectances for olive grows
For model inversion, the CCRS kindly provided its MIB
(Model Inversion of BRDF) software tool. For the linear
models, the MIB works on a matrix inversion based procedure.
For the NTAM, the modified Powell’s minimization method is
used to calculate the non-linear least squares fit in an iterative
procedure (Latifovic et al., 2003). Statistic parameters used in
the MIB are:
The statistic results of the inverse mode are very satisfying.
Figure 3 displays the coefficient of determination for the
different aggregated land cover classes. The mean coefficient of
determination for all land cover classes is 0.79 for the VIS and
0.83 for the NIR channel. Homogeneous land cover classes, e.g.
class 17: olive grows and class 24: coniferous forest, are
generally only slightly better modelled than more
heterogeneous classes. For the latter ones, the classes 12, arable
land, and 20, complex cultivation patterns may be named as
examples. This shows well how the NTAM accounts for the
varying amount of green leaf area within one vegetation class.
Model
Roujean
z
Modified Walthall
NTAM
12 13 17 20 21 22 23 24 25 26 27 28 29 31
In order to investigate the regression quality of either NOAA 15
and NOAA 16 sampling data, corresponding data sets were
separately introduced into the MIB. Mean values of the
obtained statistical parameters for all classes and channels are
displayed in table 2 and are compared between those obtained
by running the MIB with the combined sampling data set.
Observations from
NOAA 15
NOAA 16
NOAA 15 & 16
Avg R2
0.804
0.814
0.870
0.838
0.792
0.830
Channel
VIS
NIR
VIS
NIR
VIS
NIR
Avg se
0.015
0.019
0.016
0.020
0.018
0.023
Table 2: Statistical results for model inversion for different
input data sets
The input data sampling set that combines NOAA 15 and
NOAA 16 observations was also introduced into the MIB in
order to compare the performance with the Roujean and the
Modified Walthall model. Table 3 displays the corresponding
results. The NTAM yields best values for the coefficient of
0.36
0.33
0.30
0.27
0.24
0.21
0.18
0.15
0.12
0.09
0.06
0.03
0.00
0°
60°
raa
0.0
7.5
15.0
22.5
30.0
37.5
45.0
180°
52.5
120°
vza
Figure 4: Modelled VIS reflectance for olive grows where
NDVI = NDVImean - NDVIstddev
Table 3: Statistical results for model inversion for the three
different models
Another very interesting extension from the determination of
the correction parameters consists in a graphical visualization of
modelled reflectances for different sun sensor target geometries
(Sandmeier & Itten 1999, Dymond et al. 2001). Again, the land
cover class 17 (olive grows) is chosen for such a visualization.
As NTAM modelled reflectances depend on values for the
proxies αi, a criterion had to be established that allows to
display modelled reflectances for land cover typical αi values:
First, the mean αi value of the input sampling data was
calculated for the two channels. Then, the corresponding
standard deviation values were added and subtracted from the
mean αi values. The figures 4 to 7 show modelled reflectances
for the VIS and the NIR. The raa is the relative azimuth angle,
the vza the view zenith angle and the sza is the sun zenith angle.
The sza is set to the fixed value of 45 degrees in all graphics.
Note that no input data with a vza > 45° are introduced.
Modelling to a vza of 52.5° is done to demonstrate model
behaviour outside the range of calibration. The displayed
graphics allow to estimate seasonal and angular dependency of
the BRDF on different land covers. The hot spot is clearly
distinguishable in all graphics.
0.36
0.33
0.30
0.27
0.24
0.21
0.18
0.15
0.12
0.09
0.06
0.03
0.00
0°
60°
raa
120°
180°
52.5
Figure 3: Coefficient of determination for the different
aggregated land cover classes (left column= VIS,
right column= NIR)
Avg se
0.016
0.025
0.016
0.024
0.018
0.023
0.0
0
7.5
0,2
15.0
0,4
Avg R2
0.545
0.729
0.535
0.721
0.792
0.830
Channel
VIS
NIR
VIS
NIR
VIS
NIR
22.5
0,6
30.0
0,8
37.5
1
45.0
Coefficient of determination
determination, especially in the VIS channel. However, this is
not too surprising as neither the Roujean model nor the MWM
were designed to cope with sample data encompassing the
entire growing season.
vza
Figure 5: Modelled VIS reflectance for olive grows where
NDVI = NDVImean + NDVIstddev
vza
Figure 6: Modelled NIR reflectance for olive grows where
NIR – VIS = (NIR – VIS) mean – (NIR – VIS)stddev
4. CONCLUSIONS
It has been shown that the NTAM possesses a big potential to
reduce BRDF effects in AVHRR imagery of Spain. This is
quantitatively expressed by the good results in model inversion
for the two channels and on practically all land cover classes.
Apart from the good results, the main advantages of the NTAM
are its physical foundations and its simplicity, as only one set of
parameters for land cover class and channel has to be provided
to correct for the whole vegetation period.
The derived correction parameters offer a great potential for
interpretation of land cover specific biophysical properties.
Results of the forward mode of BRDF correction are not
discussed in this paper. Future work should address the
transition pixel problem which is enhanced in the forward mode
of BRDF correction. As landscape in Spain is obviously
structured on a larger scale than Canada, the land cover based
approach is to be further investigated.
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ACKNOWLEDGEMENTS
I would like to thank those people who contributed to this work
with their help and advice. First of all, I owe thanks to Prof. Dr.
Emilio Chuvieco and the staff from his institute for utter
support and scientific conduct. In addition, I like to thank
Rasim Latifovic and Josef Cihlar from the CCRS for providing
the model inversion software.